Quote from: XinXan on March 09, 2015, 03:14:49 PM

Honestly house edge doesnt even matter that much, you would lose even with 0% house edge using martingale.

Well, this is interesting.

My gut reaction upon reading that was that you are wrong: with 0% house edge you are equally likely to double-up or bust. Because with a 0% house edge the casino's expected profit is 0 regardless of how you play.

So I wrote another simulation. It simulates a player with 15 chips using martingale, starting with bets of 1, doubling on loss, betting at a 0% edge casino.

To my surprise he doubles up 38% of the time and busts 62% of the time.

Can anyone explain how that could be? Is the casino actually making a decent profit from this 0% edge game? I don't believe it.

Here's the code:

Code:

#!/usr/bin/env python

import random

start = 15 # starting bankroll
target = 30 # target bankroll
base = 1 # starting bet
rounds = wins = 0

while True:
   bankroll = start
   bet = base
   rounds += 1

   while True:
   if random.random() < 0.5: # we won
   bankroll += bet # award winnings
   bet = base # reset
   if bankroll >= target: # we reached the target
   wins += 1
   break
   else: # we lost
   bankroll -= bet # subtract loss
   bet *= 2 # double bet
   if bet > bankroll: # we can't afford the next bet
   break

   if rounds % 100000 == 0:
   print "%6d wins out of %6d rounds (%6.3f%%)" % (wins, rounds, wins * 100.0 / rounds)

and the output:

Code:

37662 wins out of 100000 rounds (37.662%)
75430 wins out of 200000 rounds (37.715%)
113539 wins out of 300000 rounds (37.846%)
151692 wins out of 400000 rounds (37.923%)
189569 wins out of 500000 rounds (37.914%)